Complex Gaussian functions expansion method applied to truncated Gaussian beams

Abstract

An analytical expression for the beam propagation factor (M ² factor) of truncated Gaussian beams was derived by using the complex Gaussian functions expansion method. The reasonability of the approximation of complex Gaussian functions expansion method is studied, and a comparison of this method with the generalised truncated second-order moments method and the asymptotic analysis method is also made. In general, an easy analytical expression for the M ² factor of truncated laser beams can be derived by using the complex Gaussian functions expansion method. The M ² factor obtained by using the complex Gaussian functions expansion method is more consistent with that in practice than that obtained by using two other methods. The analytical results obtained by using the complex Gaussian functions expansion method can be reduced to that for the non-truncated case when the truncation parameter is sufficiently large. Therefore, the complex Gaussian functions expansion method is a suitable approximation method for studying the M ² factor of truncated laser beams.

Keywords:

• complex Gaussian functions expansion method
• beam propagation factor
• truncated laser beam
• generalised truncated second-order moments method
• asymptotic analysis method

Acknowledgements

This research was supported by Open Research Fund of Key Laboratory of Atmospheric Composition and Optical Radiation of Chinese Academy of Sciences under Grant JJ-10-08, and by the National Natural Science Foundation of China under Grant 60778048, and by the Research Foundation of Sichuan Normal University of China under Grant 10DXL01.